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added link to rijkes now published HoTT book

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Rachel Lambda Samuelsson 2022-12-22 18:17:00 +01:00
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_posts/2022-12-15-haskell-and-logic.md
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@ -149,6 +149,6 @@ If you've made it this far, then congratulations! Even though I've tried to make
This blog post only covers propositional logic, but one can interpret predicate logic and even higher-order logic within programming languages. This is done with dependent type theory. In dependent type theories, types may themselves *depend* upon values, letting one create types such as `is-even n` which depend on a natural number `n`. This type would have terms which are witnesses that `n` is even. These programming languages, or proof assistants as they are usually called, enable you to prove properties of both programs and mathematical objects. In doing so they provide a way to automatically check mathematical proofs for correctness. There are already many mathematicians using these tools to create formalized proofs of mathematical theorems.
If you are interested in learning more about dependent type theory, then you might be interested in downloading and playing around with a proof assistant. I recommend [agda](https://agda.readthedocs.io/en/latest/getting-started/installation.html) to those familiar with Haskell; a lengthy [list of agda tutorials](https://agda.readthedocs.io/en/latest/getting-started/tutorial-list.html) is included in its documentation. If you wish to learn more about how doing math with types rather than sets might lead to new insights and connections to topology, then I encourage you to learn about homotopy type theory, for which there are some great resources: [HoTTEST Summer School 2022 lectures](https://www.youtube.com/playlist?list=PLtIZ5qxwSNnzpNqfXzJjlHI9yCAzRzKtx), [HoTTEST Summer School 2022 GitHub](https://github.com/martinescardo/HoTTEST-Summer-School), [1lab](https://1lab.dev/1Lab.intro.html), [HoTT Book](https://homotopytypetheory.org/book/), [Egbert Rijkes HoTT intro book](https://github.com/EgbertRijke/HoTT-Intro) (note that this is an older version of Egberts Book, the final version is expected to be published soon).
If you are interested in learning more about dependent type theory, then you might be interested in downloading and playing around with a proof assistant. I recommend [agda](https://agda.readthedocs.io/en/latest/getting-started/installation.html) to those familiar with Haskell; a lengthy [list of agda tutorials](https://agda.readthedocs.io/en/latest/getting-started/tutorial-list.html) is included in its documentation. If you wish to learn more about how doing math with types rather than sets might lead to new insights and connections to topology, then I encourage you to learn about homotopy type theory, for which there are some great resources: [HoTTEST Summer School 2022 lectures](https://www.youtube.com/playlist?list=PLtIZ5qxwSNnzpNqfXzJjlHI9yCAzRzKtx), [HoTTEST Summer School 2022 GitHub](https://github.com/martinescardo/HoTTEST-Summer-School), [Introduction to Homotopy Type Theory](https://arxiv.org/abs/2212.11082), [1lab](https://1lab.dev/1Lab.intro.html), [HoTT Book](https://homotopytypetheory.org/book/).
{% endkatexmm %}